Exponential Family Tensor Factorization for Missing-Values Prediction and Anomaly Detection

In this paper, we study probabilistic modeling of heterogeneously attributed multi-dimensional arrays. The model can manage the heterogeneity by employing an individual exponential-family distribution for each attribute of the tensor array. These entries are connected by latent variables and are shared information across the different attributes. Because a Bayesian inference for our model is intractable, we cast the EM algorithm approximated by using the Laplace method and Gaussian process. This approximation enables us to derive a predictive distribution for missing values in a consistent manner. Simulation experiments show that our method outperforms other methods such as PARAFAC and Tucker decomposition in missing-values prediction for crossnational statistics and is also applicable to discover anomalies in heterogeneous office-logging data. Keywords-tensor factorization; Bayesian probabilistic model; Gaussian process; data fusion;

• Type: Journal
• Year: 2010
• Where: ICDM
• Authors: Kohei Hayashi, Takashi Takenouchi, Tomohiro Shibata, Yuki Kamiya, Daishi Kato, Kazuo Kunieda, Keiji Yamada, Kazushi Ikeda
• Keywords: Bayesian Probabilistic Model, Data Mining, Gaussian Process, ICDM 2010, Individual Exponential-family Distribution